Abstract

In the presence of space charge forces, synchrotron oscillations result in periodic modulation of the space charge tune shift, periodic crossing of betatron resonances, and particle trapping in resonance islands. The trapping effect for one-dimensional resonance is considered using classical perturbation theory and the “frozen core” approach to calculation of space charge forces. The beam losses and emittance growth are analyzed for arbitrary order resonance; the numerical results are given for the third-order resonance.

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